STA 320: Design and Analysis of Causal Studies

1. STA 320: Design and Analysis of Causal Studies Dr. Kari Lock Morgan and Dr. Fan Li Department of Statistical Science Duke University

2. Office Hours and Support • Dr. Kari Lock Morgan, kari@stat.duke.edu • Office Hours: M 3-4pm, W 3-4pm, F 1-3pm in Old Chem 216 • Dr. Fan Li, fli@stat.duke.edu • Office Hours: M 10:30-1130am, W 2-3pm in Old Chem 122 • TA: Wenjing Shi, wenjing.shi@duke.edu • Office Hours: tbd in Old Chem 211A • Statistics Education Center • Sun, Mon, Tues, Wed, Thurs 4 – 9 pm in Old Chem 211A

3. Reading • Causal Inference for Statistics and Social Sciences • By Guido W. Imbens and Donald B. Rubin • Not yet published • Draft pdf available on Sakai (do not share) • Will distribute other relevant papers

4. Assessment • Most weeks will either have a homework due or a quiz • One midterm exam: 3/5 • Final project • Grading • Homework: 20% • Quizzes: 20% • Midterm: 30% • Final project: 30%

5. Course Website • stat.duke.edu/courses/Spring14/sta320.01/ • Class materials will be posted here • Textbook, relevant papers, etc. will be posted on Sakai

6. Causality and Potential Outcomes

7. Causality? • What is causality??? • In this class we will learn… • a formal framework for causal effects • how to design studies to estimate causal effects • how to analyze data to estimate causal effects

8. Rubin Causal Model • In the class, we’ll use the Rubin Causal Model framework for causal effects • Key points: • Causality is tied to an action (intervention) • Causal effect as a comparison of potential outcomes • Assignment mechanism

9. Causal Question • What is the effect of the treatment on the outcome? • If the opposite treatment had been received, how would the outcome differ? • Example: • treatment: choosing organic produce • outcome: get cancer? (yes or no) • Question: Does choosing organic produce decrease risk of cancer?

10. Treatment • For most of this course, we will consider only two possible treatments: • Active treatment (“treatment”) • Control treatment (“control”) – often just not getting the treatment • Two treatments (including the alternative to specified treatment) must be well defined

11. Causal Questions • What is the effect of studying on test scores? • Does texting while driving cause accidents? • Does exercising in the morning give you more energy during the day? • Do students learn better in smaller classes? • Did the hook-up happen because alcohol was involved? • Come up with your own!

12. Intervention • Causality is tied to an action (or manipulation, treatment, or intervention) • “no causation without manipulation” –manipulation need not be performed, but should be theoretically possible • Treatments must be plausible as a (perhaps hypothetical) intervention • Gender? Age? Race?

13. Not Clearly Defined Causal Questions • Are parents more conservative then their children because they are older? • What is the causal effect of majoring in statistical science on future income? • Did she get hired because she is female? • Can you make these into well-defined causal questions?

14. Potential Outcomes • Key question: what would have happened, under the opposite treatment? • A potential outcome is the value of the outcome variable for a given value of the treatment • Outcome variable: Y • Y(treatment): outcome under treatment • Y(control): outcome under control

15. Potential Outcomes • Y(organic) = cancer or no cancer • Y(non-organic) = cancer or no cancer • Possibilities: Y(organic) = no cancer, Y(non-organic) = cancer Y(organic) = Y(non-organic) = cancer Y(organic) = Y(non-organic) = no cancer Y(organic) = cancer, Y(non-organic) = no cancer • Formulate the potential outcomes for your example

16. Causal Effect • The causal effect is the comparison of the potential outcome under treatment to the potential outcome under control • For quantitative outcomes, we often take a difference: Causal Effect = Y(treatment) – Y(control)

17. Causal Effect • Possibility 1: Y(organic) = no cancer, Y(non-organic) = cancer Causal effect for this individual: choosing organic produce prevents cancer, which he otherwise would have gotten eating non-organic • Possibility 2: Y(organic) = cancer, Y(non-organic) = cancer Causal effect for this individual: he would get cancer regardless, so no causal effect

18. Causal Effect • Y = test score • Y(study) – Y(don’t study) • Example: Y(study) = 90, Y(don’t study) = 60 • Causal effect = 90 – 60 = 30. Studying causes a 30 point gain in test score for this unit. • Y = accident (y/n) • Y(texting) vs Y(not texting) • Y = energy during the day • Y(morning exercise) – Y(no morning exercise) • Y = hook-up (y/n) • Y(alcohol) vs Y(no alcohol)

19. Units • These are unit-level causal effect • Unit: the person, place, or thing upon which the treatment will operate, at a particular point in time • Note: the same person at different points in time = different units • The causal effect will probably not be the same for each unit

20. Causal Effects • The definition of a causal effect does not depend on which treatment is observed • Causal effects, in their definition, do not relate to probability distribution for subjects “who got different treatments”, or to coefficients of models • Not a before-after comparison. Potential outcomes are a “what-if” comparison. • Potential outcomes may depend on other variables (not just the treatment)

21. Causal Effects • Fundamental problem in estimating causal effects: at most one potential outcome observed for each unit • The other potential outcome lies in an unobserved counterfactual land… what would have happened, under a different treatment For treated units: Y(treatment) = observed, Y(control) = ??? For control units: Y(treatment) = ???, Y(control) = observed

22. Estimation • For the definition of a causal effect: compare potential outcomes for a single unit • However, in reality, we can only see one potential outcome for each unit • For estimation of a causal effect we will need to consider multiple units, some who have been exposed to the treatment, and some to the control

23. Multiple Units • Need to compare similar units, some exposed to active treatment, and some to control • Can be same units at different points in time, or different units at the same point in time • In this class we will focus primarily on comparing different (but similar) units at the same point in time

24. Summary • Causality is tied to an action (treatment) • Potential outcomes represent the outcome for each unit under treatment and control • A causal effect compares the potential outcome under treatment to the potential outcome under control for each unit • In reality, only one potential outcome observed for each unit, so need multiple units to estimate causal effects